Scaling Motion Planning Infeasibility Proofs

TL;DR

The paper tackles the computational burden of proving infeasibility in complete motion planning by introducing a GPU-accelerated, embarrassingly parallel framework that constructs infeasibility proofs via manifold learning and Coxeter triangulation. A key contribution is batch triangulation, which manages limited GPU memory while performing triangulation and collision checking entirely on the GPU to minimize data transfer. The approach uses a fixed-size, GPU-friendly permutahedral (Coxeter) representation to enable scalable manifold tracing, and combines this with batch collision checking on exact primitive shapes to achieve substantial speedups. Experiments on 5-DoF and 6-DoF manipulators demonstrate over two orders of magnitude speedups in critical steps and show the method achieving asymptotically complete motion planning with efficient CPU-GPU cooperation, enabling application to higher-dimensional problems.

Abstract

Achieving completeness in the motion planning problem demands substantial computation power, especially in high dimensions. Recent developments in parallel computing have rendered this more achievable. We introduce an embarrassingly parallel algorithm for constructing infeasibility proofs. Specifically, we design and implement a manifold triangulation algorithm on GPUs based on manifold tracing with Coxeter triangulation. To address the challenge of extensive memory usage within limited GPU memory resources during triangulation, we introduce batch triangulation as part of our design. The algorithm provides two orders of magnitude speed-up compared to the previous method for constructing infeasibility proofs. The resulting asymptotically complete motion planning algorithm effectively leverages the computational capabilities of both CPU and GPU architectures and maintains minimum data transfer between the two parts. We perform experiments on 5-DoF and 6-Dof manipulator scenes.

Figures (9)

• Figure 1: Algorithm overview. The algorithm maximizes resource utilization by efficiently distributing its components across both CPU and GPU. The triangulation and the collision checking steps are completed entirely on GPU.
• Figure 2: Example 2D permutahedral representation, "v" for vertex, "p" for partition, for the two triangles (blue and red) in a square.
• Figure 3: The steps for locating edges from seed points.
• Figure 4: The steps for searching edges in iteration.
• Figure 5: First edge (marked in red) and its permutahedral presentation in the new triangulation, for subdivision of a 2-simplex and a 3-simplex, with $k=2$.